CN117825185A - Method and system for determining dynamic strength of brittle material - Google Patents
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Abstract
The invention relates to a method and a system for determining the dynamic strength of a brittle material, belongs to the technical field of material and structural impact dynamics, and solves the problems of complex dynamic strength determining process and low efficiency of the brittle material in the prior art. The method comprises the following steps: determining an analytical formula of the dynamic strength of the brittle material based on a modified dynamic incubation time fracture criterion; carrying out mechanical property experiments on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material; and calculating the dynamic strength of the brittle material according to the stress history curve and the dynamic inoculation time of the brittle material based on the analytic expression of the dynamic strength of the brittle material. The dynamic strength of the brittle material is obtained through rapid and accurate calculation.
Description
Technical Field
The invention relates to the technical field of material and structural impact dynamics, in particular to a method and a system for determining the dynamic strength of a brittle material.
Background
Under dynamic loading, the dynamic strength of the brittle material tends to be higher than the quasi-static strength, and the material strength gradually increases with the increase of the strain rate, i.e. the strength-strain rate enhancement effect of the brittle material. The effect of the strain rate of strength is critical when dealing with dynamic loading (e.g., in the fields of penetration mechanics, explosive mechanics, and high-speed collisions). The traditional view point considers that the rate dependence of the dynamic strength is the intrinsic property of the material, the dynamic strength of the brittle material under different strain rates can be directly measured by experiments, and can be expressed by experience or semi-experience equations, and when the stress reaches the dynamic strength, the brittle material is damaged. For a brittle material, a large number of experiments and numerical simulation researches are required to be carried out, and then dynamic strength or DIF experience and half experience rate related expressions are provided according to a large number of dynamic strength experimental data and physical mechanisms under different loading rates, so that the dynamic strength of the material is determined, the process is complex, and the efficiency is low.
Disclosure of Invention
In view of the above analysis, the embodiments of the present invention aim to provide a method and a system for determining the dynamic strength of a brittle material, which are used for solving the problems of complex dynamic strength determining process and low efficiency of the existing brittle material.
In one aspect, an embodiment of the present invention provides a method for determining a dynamic strength of a brittle material, including the steps of:
determining an analytical formula of the dynamic strength of the brittle material based on a modified dynamic incubation time fracture criterion;
carrying out mechanical property experiments on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material;
and calculating the dynamic strength of the brittle material according to the stress history curve and the dynamic inoculation time of the brittle material based on the analytic expression of the dynamic strength of the brittle material.
Based on the further improvement of the method, mechanical property experiments are carried out on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material, and the method comprises the following steps:
performing a quasi-static mechanical property experiment on the brittle material to obtain the quasi-static strength of the material;
carrying out dynamic mechanical property experiments on the brittle material to obtain a stress history curve of the brittle material;
and calculating the dynamic inoculation time of the brittle material according to the quasi-static strength and stress history curve of the material.
Based on a further improvement of the method, the dynamic incubation time of the brittle material is calculated according to the following formula:
，
wherein,time of quasi-static loading is indicated, +.>Indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Indicating the dynamic incubation time of the brittle material.
Based on further improvement of the method, dynamic mechanical property experiments are carried out on the brittle material under different loading rates, and historical stress curves under different loading rates are obtained;
calculating the dynamic inoculation time of the brittle material according to the quasi-static strength and stress history curve of the material, wherein the dynamic inoculation time comprises the following steps:
calculating dynamic inoculation time under different loading rates according to the quasi-static strength and stress history curves under different loading rates;
and obtaining the final dynamic inoculation time of the brittle material according to the dynamic inoculation time under different loading rates.
Based on further improvement of the method, the dynamic inoculation time under different loading rates is averaged to obtain the final dynamic inoculation time of the brittle material.
Based on a further improvement of the method, the modified dynamic incubation time fracture criteria are expressed as:wherein->Time of quasi-static loading is indicated, +.>Indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Representing the dynamic incubation time.
Based on a further improvement of the method, when the stress history curve is a linear slope type curve, determining the analytical formula of the dynamic strength of the brittle material based on the modified dynamic incubation time fracture criterion is:
wherein->Representing the quasi-static strength of the brittle material, +.>The dynamic inoculation time is represented by the time of the dynamic inoculation,representing the dynamic strength of the brittle material, +.>Indicating the loading rate of the brittle material.
Based on the further improvement of the method, when the stress history curve is a quadratic curve, if damage occurs in a loading section of the quadratic stress, determining an analytical formula of the dynamic strength of the brittle material based on a modified dynamic inoculation time fracture criterion is as follows:
；/>；
if the damage occurs at the amplitude of the quadratic stress, determining the analytical formula of the dynamic strength of the brittle material based on the modified dynamic incubation time fracture criterion as follows:
；
；
wherein,representing the quasi-static strength of the brittle material, +.>Indicates dynamic incubation time,/->Representing the dynamic strength of the brittle material, +.>Indicating the time for the stress to reach amplitude, +.>Representing stress amplitude +.>Representing the loading rate.
In another aspect, an embodiment of the present invention provides a system for determining dynamic strength of a brittle material, including:
the analytic determination module is used for determining an analytic of the dynamic strength of the brittle material based on the modified dynamic inoculation time fracture criterion;
the experimental module is used for carrying out mechanical property experiments on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material;
the dynamic strength determining module is used for calculating the dynamic strength of the brittle material according to the stress history curve and the dynamic inoculation time of the brittle material based on the analytic expression of the dynamic strength of the brittle material.
Based on a further improvement of the above system, the modified dynamic incubation time break-off criterion is expressed as:wherein->Time of quasi-static loading is indicated, +.>Indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Representing the dynamic incubation time.
Compared with the prior art, the method for determining the dynamic strength of the brittle material provided by the embodiment determines the analytic expression of the dynamic strength of the brittle material based on the correction type dynamic inoculation time breaking criterion, obtains the dynamic inoculation time of the brittle material through dynamic mechanical property experiments, can quickly and accurately calculate the dynamic strength of the brittle material according to the stress history curve and the damage inoculation time of the brittle material, does not need to carry out a large number of experiments, and is simple in method and convenient to implement.
In the invention, the technical schemes can be mutually combined to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to designate like parts throughout the drawings;
FIG. 1 is a flow chart of a method for determining dynamic strength of a brittle material according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a material failure occurring in a loading section of a quadratic stress history curve according to an embodiment of the present invention;
FIG. 3 is a graph showing the lower tensile stress history and the breaking time according to an embodiment of the present invention;
FIG. 4 is a graph showing the dynamic tensile strength results in an embodiment of the present invention;
FIG. 5 is a graph showing the dynamic compressive strength results in an embodiment of the present invention;
FIG. 6 is a block diagram of a system for dynamic strength determination of brittle materials according to an embodiment of the present invention.
Detailed Description
Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form a part hereof, and together with the description serve to explain the principles of the invention, and are not intended to limit the scope of the invention.
In one embodiment of the present invention, a method for determining the dynamic strength of a brittle material is disclosed, as shown in fig. 1, comprising the steps of:
s1, determining an analytic formula of the dynamic strength of the brittle material based on a modified dynamic inoculation time fracture criterion;
s2, carrying out mechanical property experiments on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material;
s3, based on the analytic expression of the dynamic strength of the brittle material, calculating the dynamic strength of the brittle material according to the stress history curve and the dynamic inoculation time of the brittle material.
Compared with the prior art, the method for determining the dynamic strength of the brittle material provided by the embodiment determines the analytic expression of the dynamic strength of the brittle material based on the correction type dynamic inoculation time breaking criterion, obtains the dynamic inoculation time of the brittle material through dynamic mechanical property experiments, can quickly and accurately calculate the dynamic strength of the brittle material according to the stress history curve and the damage inoculation time of the brittle material, does not need to carry out a large number of experiments, and is simple in method and convenient to implement.
The stress time integral dynamic failure criterion can be generally expressed in the following form:
；
in the method, in the process of the invention,for the stress history curve at the material failure location as measured by the material dynamic mechanical properties experiment, t is the time counted from the stress loading at the material failure location, +.>Indicating the start of integration, +.>Indicating the moment of material destruction, i.e->To achieve dynamic strength for stress at the failure location>N is the thermal activation correlation coefficient of the material, n=1, and c is a constant. Wherein due to the pair t<The physical meaning of stress time integration in the 0 period is lacking, so +.>Needs to meet->。
In the prior art, the starting moment of integration is shownAccording to->Determination of->The dynamic inoculation time is represented and is obtained by combining dynamic inoculation criteria with material mechanics experimental results. Due to the presence of the stress-strain rate enhancing effect of the brittle material, < >>Will gradually decrease with increasing load rate, resulting in a +.>The situation, namely the original criterion integration interval [ +.>,/>]Exceeding the actual time range of action of the load [0, ] -the load>]To ensure that the original rule is satisfied [ ->,/>]∈[0, />]Existing guidelines will be limited to low load rate load ranges and therefore only work at low load rates.
The linear ramp stress history load is an idealized ramp load, and in many theoretical and experimental studies, to facilitate the study of the effect of the strength strain rate, the nonlinear ramp stress history curve is typically approximated as a linear ramp curve to obtain a curve slope or loading rate that does not change over time. Therefore, the stress threshold corresponding to the integral starting moment in the criterion is determined through the linear slope stress history curve.
When the stress-time curve at the failure location is a linear ramp, i.eWherein->For the loading rate, substituting it into the above formula (1) yields:
；/>；
the expression of the material stress or dynamic strength at the breaking moment under the linear slope stress history loading with respect to the loading rate is obtained by solving the following:
；
wherein,the stress value at the start of integration is indicated.
Under quasi-static and dynamic loading, the damage of brittle materials needs to ensure that the stress reaches the quasi-static strength. Therefore, at any loading rate, the dynamic strength needs to constantly satisfy the following relationship:
；
in quasi-static loading) In the following formula (4), i.e. +.>The following steps are:
；
in response to this, the control unit,i.e. +.>。
Thus, the stress time integral dynamic failure criterion is further written as:
；
when loaded with a ramp stress history of magnitude equal to the quasi-static strength, i.e
；
Substitution criterion (5) is available:
；
in the incubation time fracture criterion, the amplitude duration value is equal to the material parameter incubation when loaded with a ramp stress history having an amplitude equal to the quasi-static strengthTime of incubation. Based on this, it is further possible to:
；
normally n=1, a modified dynamic incubation time break-off criterion is obtained, specifically:
；
time of quasi-static loading is indicated, +.>Indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Representing the dynamic incubation time.
Because the amplitude of the loading stress is constant and is the amplitude when the stress is in quasi-static strength, the duration is the inoculation time of the material parameters, and for convenience, the loading stress at the material breaking position reaches the quasi-static strength and the process time of the material breaking is reachedCalled dynamic incubation time->The material parameter inoculation time is the characteristic value of the dynamic inoculation time under the condition that the stress amplitude is constant and the quasi-static strength is loaded, so that the quasi-static strength is obtainedThen this is referred to as a modified dynamic incubation time criterion. Compared with the prior art, the method is applicable to the wide loading rate range based on the modified dynamic inoculation time fracture criterion while the influence of stress history on the dynamic strength of the brittle material is reflected by considering the time correlation problem, and the limit condition of the loading rate application range is not existed.
After the modified dynamic inoculation time criterion is obtained, determining an analytic formula of the dynamic strength of the brittle material based on the modified dynamic inoculation time fracture criterion.
When the stress history curve of the brittle material is a linear slope curve, determining an analytic formula of the dynamic strength of the brittle material based on a modified dynamic inoculation time fracture criterion is as follows:
wherein->Representing the quasi-static strength of the brittle material, +.>The dynamic inoculation time is represented by the time of the dynamic inoculation,representing the dynamic strength of the brittle material, +.>Indicating the loading rate of the brittle material.
When the stress history curve is a linear slope, the dynamic strength of the brittle material fracture is obtained according to formula (7). It should be noted that for the linear ramp stress history curve, +.>Then->。
When the stress history curve is quadratic, the quadratic stress history curve is expressed as:
；
where k is the loading parameter and k< 0，Representing the quadratic half period, i.e. the time for which the stress reaches the amplitude,/->Representing the stress amplitude.
Assuming that material failure occurs at the failure location at the secondary stress loading section, i.eAs shown in fig. 2. At the position of destruction->The stress at the moment is dynamic bearing capacity or dynamic strength +.>The following steps are:
；
；
；
the average loading rate at the breaking position is adopted as the loading rate under the quadratic loading, and the strain rate expression is obtained by Hooke's lawAnd satisfy->The relation, where E represents Young's modulus, whereby +.>Bringing equations (9) and (11) back, the load factor is expressed as:
；
substituting the quadratic stress history curve into the dynamic inoculation time criterion to obtain the following steps:
；
solving to obtainAppropriate solutions to the stress history curve parameters (amplitude and period) (i.e.)>Solution constant positive value) is:
；
to further obtainThe expressions for the loading rates are linked (10), (11) and (12) to give a relationIs a unitary fourth-order equation of:
，
wherein,
，/>，
，/>，
，
solving to obtainSuitable solutions for the load rate are:
；
；
will beCarrying in formula (14) to obtain +.>Expression for load rate
；
When the failure occurs at the magnitude of the quadratic stress,=/>，/>regarding load rateIs a proper solution (i.e.)>Solutions constantly greater than 0) are:
；
wherein,
；
when (when)At a limited loading rate, the quadratic ramp loading tends to be linear ramp loading, in which case +.>The solution for the load rate is:
。
after the analytic expression of the dynamic strength is obtained, carrying out a dynamic performance experiment on the brittle material to obtain the dynamic inoculation time of the brittle material, and calculating the dynamic strength of the brittle material according to the dynamic inoculation time of the brittle material.
Specifically, mechanical property experiments are carried out on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material, and the method comprises the following steps:
s21, performing a quasi-static mechanical property experiment on the brittle material to obtain the quasi-static strength of the material;
s22, carrying out dynamic mechanical property experiments on the brittle material to obtain a stress history curve of the brittle material;
s23, calculating the dynamic inoculation time of the brittle material according to the quasi-static strength and stress history curve of the material.
In the dynamic incubation time fracture criterion, the dynamic incubation time of brittle materials is one of the important material parameters, and when using this criterion, the dynamic incubation time value needs to be determined. And carrying out mechanical property experiments on the brittle material to obtain the dynamic inoculation time of the brittle material.
In the implementation, the quasi-static loading of the material is realized through a material static mechanical experiment (such as a universal experiment machine), and the quasi-static strength of the material can be obtained according to the stress-strain curve of the material measured through the experiment.
In the implementation, a split Hopkinson bar (Split Hopkinson Bar, SHPB) experimental system can be used for carrying out dynamic mechanical property experiments on the brittle material. The SHPB device is typically composed of a light air cannon, a bullet, an incident beam, a transmission beam, a dynamic strain gauge, a damping beam, and a damper. The light air cannon controls the bullet to emit at a certain speed, and after the bullet collides with the incident rod, the generated incident pulse propagates in the rod, and as the wave impedance of the incident rod is different from that of the test piece, part of waves after the incident wave collides with the interface in the propagation process of the incident wave return along the original path to form reflected waves, and the other part of waves continuously propagate into the test piece through the interface to form transmitted waves. The stress wave introduced into the test piece repeatedly propagates, penetrates at the interface position of the material and the transmission rod, and forms transmission wave in the transmission rod.
Experimental pulse signals are acquired through strain gauges and dynamic strain gauges on the incidence rod and the transmission rod, and stress history curves of the brittle material under different loading conditions can be obtained through three-wave method calculation.
Under ideal conditions, the dynamic inoculation time can be obtained by only one stress history curve, and in the experiment, if the brittle material meets the dynamic inoculation time criterion and is damaged dynamically, the brittle material has the following characteristics
；
In the method, in the process of the invention,representing stress history curve>The moment of material failure in the experiment is shown. />Time of quasi-static loading is indicated, +.>Representing the quasi-static strength of the brittle material, +.>Indicating incubation time. The corresponding moment when the stress reaches the quasi-static strength is the quasi-static loading time +.>。
However, considering the heterogeneity of the material, in order to further improve the accuracy of calculation, a dynamic mechanical property experiment is performed on the brittle material under different loading rates, so as to obtain a historical stress curve under different loading rates;
calculating dynamic inoculation time under different loading rates according to the quasi-static strength and stress history curves under different loading rates;
and obtaining the final dynamic inoculation time of the brittle material according to the dynamic inoculation time under different loading rates.
When the method is implemented, dynamic mechanical property experiments can be carried out on the brittle material at 2-5 different loading rates to obtain 2-5 corresponding dynamic inoculation times, and then the final dynamic inoculation time of the brittle material is obtained by averaging.
For example, 3 stress history curves were obtained by performing dynamic mechanical property experiments with 3 sets of different loading rates. Calculating the dynamic inoculation time under 3 groups of different loading rates according to the formula (20), and averaging the dynamic inoculation time under 3 groups of different loading rates to obtain the final dynamic inoculation time of the brittle material.
It should be noted that, different inoculation time values can be obtained from experimental stress history curves under different loading rates, which are considered to be caused by material heterogeneity, and the different values form inoculation time estimation errors, and an average value can be taken as an inoculation time parameter used by a criterion.
After the dynamic inoculation time of the brittle material is obtained, the dynamic strength of the brittle material is calculated according to the stress history curve and the dynamic inoculation time of the brittle material based on the analysis type of the dynamic strength of the brittle material.
Namely, the stress history curve and the dynamic inoculation time of the brittle material are brought into the analysis type of the dynamic strength, and the dynamic strength of the brittle material can be obtained.
Taking a Fangshan Marble (FM) rock material and a LongXuan sandstone (Longyou sandstone, LS) rock material in the literature as an example, comparing the dynamic strength calculation result under the quadratic stress history obtained by the rule with the experimental result in the existing literature respectively, and verifying the applicability of the dynamic inoculation time fracture rule.
Stress history curves of two rock materials under a certain loading rate, which are measured through dynamic mechanical strength experiments (Hopkins rod experiments), are combined with quasi-static strength of the materialsDynamic incubation time of the available material +.>. Taking the tensile experimental parameters of the mountain marble as an example, obtaining a tensile stress history curve and breaking time +.>As shown in FIG. 3, stretch +.>The estimated value was 75.5. Mu.s. Similarly, the tensile material parameters of the Longxue sandstone are calculated as follows: />= 3.5MPa，/>=57.5 μs; the parameters of the compression materials of the mountain marble are as follows: />= 155MPa，/>=44.6 μs; the compression material parameters of the Longxue sandstone are as follows: /> = 31MPa，/>= 48.2μs。
Fig. 4 is a graph comparing the dynamic tensile strength calculation result with the experimental result of the literature, wherein (a) is the comparison result of the dynamic tensile bearing capacity calculation value and the experimental data of the mountain marble material, and (b) is the comparison result of the dynamic tensile bearing capacity calculation value and the experimental data of the long run sandstone material. In the figure, the solid line is the calculation result under the loading of the quadratic slope amplitude infinity (linear slope), the broken line is the calculation result when the damage occurs at the quadratic slope amplitude, the dash-dot line is the calculation result when the amplitude takes a certain value, and the gray area is the numerical value area under the loading of the quadratic slope with different amplitudes. As can be seen from fig. 4, the tensile calculation result is better matched with the experimental result. Fig. 5 is a graph comparing the dynamic compression strength calculation result with the experimental result of the literature, wherein (a) is a comparison result of the dynamic compression bearing capacity calculation value and the experimental data of the mountain marble material, and (b) is a comparison result of the dynamic compression bearing capacity calculation value and the experimental data of the long-run sandstone material. Similarly, as can be seen from fig. 5, the compression calculation result is better matched with the experimental result.
It can be seen that the dynamic incubation time fracture criterion established by the invention has applicability and feasibility in judging the dynamic strength of the brittle material. Meanwhile, the strength calculation result obtained by the criterion shows that the dynamic strength of the material is calculated amount related to the stress history curve, so that if the brittle material strength is judged by the dynamic strength failure criterion, the dynamic strength of the brittle material can be quickly and accurately obtained when the stress history curve corresponding to the dynamic strength obtained by the experimental test is provided.
In one embodiment of the present invention, a system for determining the dynamic strength of a brittle material is disclosed, as shown in FIG. 6, comprising the following modules:
the analytic determination module is used for determining an analytic of the dynamic strength of the brittle material based on the modified dynamic inoculation time fracture criterion;
the experimental module is used for carrying out mechanical property experiments on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material;
the dynamic strength determining module is used for calculating the dynamic strength of the brittle material according to the stress history curve and the dynamic inoculation time of the brittle material based on the analytic expression of the dynamic strength of the brittle material.
Preferably, the modified dynamic incubation time break-off criteria are expressed as:wherein->Time of quasi-static loading is indicated, +.>Indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Representing the dynamic incubation time.
The method embodiment and the system embodiment are based on the same principle, and the related parts can be mutually referred to and can achieve the same technical effect. The specific implementation process refers to the foregoing embodiment, and will not be described herein.
Those skilled in the art will appreciate that all or part of the flow of the methods of the embodiments described above may be accomplished by way of a computer program to instruct associated hardware, where the program may be stored on a computer readable storage medium. Wherein the computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (10)
1. A method for determining the dynamic strength of a brittle material, comprising the steps of:
determining an analytical formula of the dynamic strength of the brittle material based on a modified dynamic incubation time fracture criterion;
carrying out mechanical property experiments on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material;
and calculating the dynamic strength of the brittle material according to the stress history curve and the dynamic inoculation time of the brittle material based on the analytic expression of the dynamic strength of the brittle material.
2. The method of claim 1, wherein the mechanical property experiment is performed on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material, and the method comprises the following steps:
performing a quasi-static mechanical property experiment on the brittle material to obtain the quasi-static strength of the material;
carrying out dynamic mechanical property experiments on the brittle material to obtain a stress history curve of the brittle material;
and calculating the dynamic inoculation time of the brittle material according to the quasi-static strength and stress history curve of the material.
3. The method of claim 2, wherein the dynamic incubation time of the brittle material is calculated according to the following formula:
；
wherein,time of quasi-static loading is indicated, +.>Indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Indicating the dynamic incubation time of the brittle material.
4. The method for determining the dynamic strength of a brittle material according to claim 2, wherein the brittle material is subjected to dynamic mechanical property experiments under different loading rates to obtain historical stress curves under different loading rates;
calculating the dynamic inoculation time of the brittle material according to the quasi-static strength and stress history curve of the material, wherein the dynamic inoculation time comprises the following steps:
calculating dynamic inoculation time under different loading rates according to the quasi-static strength and stress history curves under different loading rates;
and obtaining the final dynamic inoculation time of the brittle material according to the dynamic inoculation time under different loading rates.
5. The method of claim 4, wherein the dynamic incubation times at different loading rates are averaged to obtain a final dynamic incubation time for the brittle material.
6. The method of claim 1, wherein the modified dynamic incubation time fracture criteria is expressed as:wherein->Indicating the moment of the quasi-static loading,indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Representing the dynamic incubation time.
7. The method of claim 6, wherein when the stress history curve is a linear ramp type curve, determining the analytical formula of the dynamic strength of the brittle material based on the modified dynamic incubation time fracture criteria is:
wherein->Representing the quasi-static strength of the brittle material, +.>Indicates dynamic incubation time,/->Representing the dynamic strength of the brittle material, +.>Indicating the loading rate of the brittle material.
8. The method according to claim 6, wherein when the stress history curve is a quadratic curve, if the damage occurs in a loading section of the quadratic stress, determining the analytical formula of the dynamic strength of the brittle material based on the modified dynamic incubation time fracture criteria is:
，
，
if the damage occurs at the amplitude of the quadratic stress, determining the analytical formula of the dynamic strength of the brittle material based on the modified dynamic incubation time fracture criterion as follows:
；
；
wherein,indicating brittlenessQuasi-static strength of sexual material->Indicates dynamic incubation time,/->Representing the dynamic strength of the brittle material, +.>Indicating the time for the stress to reach amplitude, +.>Representing stress amplitude +.>Representing the loading rate.
9. A system for determining the dynamic strength of a brittle material, comprising the following modules:
the analytic determination module is used for determining an analytic of the dynamic strength of the brittle material based on the modified dynamic inoculation time fracture criterion;
the experimental module is used for carrying out mechanical property experiments on the brittle material to obtain a dynamic inoculation time and stress history curve of the brittle material;
the dynamic strength determining module is used for calculating the dynamic strength of the brittle material according to the stress history curve and the dynamic inoculation time of the brittle material based on the analytic expression of the dynamic strength of the brittle material.
10. The system for dynamic strength determination of brittle material according to claim 9, characterized in that the modified dynamic incubation time break-off criterion is expressed as:wherein->Time of quasi-static loading is indicated, +.>Indicating the moment of destruction of the brittle material, +.>Stress history curve representing brittle material, +.>Representing the quasi-static strength of the brittle material, +.>Representing the dynamic incubation time.
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|---|---|---|---|
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| US20220075911A1 (en) * | 2020-06-11 | 2022-03-10 | Dalian University Of Technology | Method for predicting structural failure by strength-criterion-driven peridynamic model |
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